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This article is cited in 16 scientific papers (total in 16 papers)
Poincaré map for some polynomial systems of differential equations
V. P. Varin M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences
Abstract:
One approach to the classical problem of distinguishing between a centre and a focus for a system of differential equations with polynomial right-hand sides in the plane is discussed. For a broad class of such systems necessary and sufficient conditions for a centre are expressed in terms of equations in variations of higher order. By contrast with the existing methods of investigation, attention is concentrated on the explicit calculation of the asymptotic behaviour of the Poincaré map rather than on finding sufficient centre conditions
as such; this also enables one to study bifurcations of birth of arbitrarily strongly degenerate cycles.
Received: 18.06.2003 and 15.01.2004
Citation:
V. P. Varin, “Poincaré map for some polynomial systems of differential equations”, Sb. Math., 195:7 (2004), 917–934
Linking options:
https://www.mathnet.ru/eng/sm832https://doi.org/10.1070/SM2004v195n07ABEH000832 https://www.mathnet.ru/eng/sm/v195/i7/p3
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